Question

Find the sum of 5x+20 and the opposite.write an equivalent expression in standard form justify each step

Answer 1

• Therefore, the sum of 5x+20 and the opposite is: 0

• Thus, the equivalent expression is:

`5x+20-\left(5x+20\right)=0`

Explanation:

• We know that the opposite is the additive inverse.

• For example, 8+(−8)=0 where 0 is the identity for addition.

Given that we have to compute the sum of 5x+20 and the opposite.

Given

• 5x+20

• opposite of 5x+20 = -(5x+20)

so

The sum of 5x+20 and the opposite:

5x+20 + -(5x+20)

Distribute the Negative Sign

`=5x+20+-1\left(5x+20\right)`

`=5x+20+-1\left(5x\right)+\left(-1\right)\left(20\right)`

`=5x+20+-5x+-20`

Combine Like Terms

`=5x+20+-5x+-20`

`=\left(5x+-5x\right)+\left(20+-20\right)`

`=0+0`

`=0`

• Therefore, the sum of 5x+20 and the opposite is: 0

• Thus, the equivalent expression is:

`5x+20-\left(5x+20\right)=0`